Converting font contour curves
A system includes a computing device that includes a memory configured to store instructions. The system also includes a processor to execute the instructions to perform operations that include receiving data representative of a portion of a font character. The portion of the font character being represented as one or more cubic curves. Operations also include determining one or more quadratic curves that approximately track the shape of the one or more cubic curves. In a geometric and recursive manner, determining the one or more quadratic curves includes using a predefined tolerance to compare the one or more quadratic curves to the one or more cubic curves. Operations also include preparing data to represent the one or more quadratic curves to represent the portion of the font character.
1. A computing device implemented method comprising:
receiving data representative of a portion of a font character, the portion of the font character being represented as one or more cubic curves;
in a geometric and recursive manner, determining two or more quadratic curves that approximately track the shape of the one or more cubic curves, wherein determining the two or more quadratic curves includes identifying one or more points located at a midpoint between other points defining and located on the two or more quadratic curves and using a predefined tolerance to compare the two or more quadratic curves to the one or more cubic curves; and
preparing data to represent the two or more quadratic curves to represent the portion of the font character, wherein the prepared data is absent data representing the one or more points located at the midpoint between the other points defining the two or more quadratic curves.
2. The computing device implemented method of claim 1 , wherein the one or more cubic curves are cubic Bezier curves.
3. The computing device implemented method of claim 1 , wherein the two or more quadratic curves are quadratic Bezier curves.
4. The computing device implemented method of claim 1 , wherein at least one point defining one of the two or more quadratic curves is located at a midpoint between two other points.
5. The computing device implemented method of claim 4 , wherein the at least one point is located on a tangent to one of the two or more quadratic curves.
6. The computing device implemented method of claim 1 , wherein the predefined tolerance is user specified.
7. The computing device implemented method of claim 1 , wherein the predefined tolerance represents the maximal orthogonal distance between at least one of the one or more cubic curves and at least one of the two or more quadratic curves.
8. The computing device implemented method of claim 1 , wherein each of the one or more cubic curves is defined by at least four points.
9. The computing device implemented method of claim 1 , wherein each of the two or more quadratic curves is defined by at least three points.
10. The computing device implemented method of claim 1 , wherein the other points defining the two or more quadratic curves are control points.
11. A system comprising:
a computing device comprising:
a memory configured to store instructions; and
a processor to execute the instructions to perform operations comprising:
receiving data representative of a portion of a font character, the portion of the font character being represented as one or more cubic curves;
in a geometric and recursive manner, determining two or more quadratic curves that approximately track the shape of the one or more cubic curves, wherein determining the two or more quadratic curves includes identifying one or more points located at a midpoint between other points defining and located on the two or more quadratic curves and using a predefined tolerance to compare the two or more quadratic curves to the one or more cubic curves; and
preparing data to represent the two or more quadratic curves to represent the portion of the font character, wherein the prepared data is absent data representing the one or more points located at the midpoint between the other points defining the two or more quadratic curves.
12. The system of claim 11 , wherein the one or more cubic curves are cubic Bezier curves.
13. The system of claim 11 , wherein the two or more quadratic curves are quadratic Bezier curves.
14. The system of claim 11 , wherein at least one point defining one of the two or more quadratic curves is located at a midpoint between two other points.
15. The system of claim 14 , wherein the at least one point is located on a tangent to one of the two or more quadratic curves.
16. The system of claim 11 , wherein the predefined tolerance is user specified.
17. The system of claim 11 , wherein the predefined tolerance represents the maximal orthogonal distance between at least one of the one or more cubic curves and at least one of the two or more quadratic curves.
18. The system of claim 11 , wherein each of the one or more cubic curves is defined by at least four points.
19. The system of claim 11 , wherein each of the two or more quadratic curves is defined by at least three points.
20. The system of claim 11 , wherein the data absent from the data prepared to represent the two or more quadratic curves represents at least one point located at a midpoint between two control points.
21. The system of claim 11 , wherein the other points defining the two or more quadratic curves are control points.
22. One or more non-transitory computer readable media storing instructions that are executable by a processing device, and upon such execution cause the processing device to perform operations comprising:
receiving data representative of a portion of a font character, the portion of the font character being represented as one or more cubic curves;
in a geometric and recursive manner, determining two or more quadratic curves that approximately track the shape of the one or more cubic curves, wherein determining the two or more quadratic curves includes identifying one or more points located at a midpoint between other points defining and located on the two or more quadratic curves and using a predefined tolerance to compare the two or more quadratic curves to the one or more cubic curves; and
preparing data to represent the one or more quadratic curves to represent the portion of the font character, wherein the prepared data is absent data representing the one or more points located at the midpoint between the other points defining the two or more quadratic curves.
23. The non-transitory computer readable media of claim 22 , wherein the one or more cubic curves are cubic Bezier curves.
24. The non-transitory computer readable media of claim 22 , wherein the two or more quadratic curves are quadratic Bezier curves.
25. The non-transitory computer readable media of claim 22 , wherein at least one point defining one of the two or more quadratic curves is located at a midpoint between two other points.
26. The non-transitory computer readable media of claim 25 , wherein the at least one point is located on a tangent to one of the two or more quadratic curves.
27. The non-transitory computer readable media of claim 22 , wherein the predefined tolerance is user specified.
28. The non-transitory computer readable media of claim 22 , wherein the predefined tolerance represents the maximal orthogonal distance between at least one of the one or more cubic curves and at least one of the two or more quadratic curves.
29. The non-transitory computer readable media of claim 22 , wherein each of the one or more cubic curves is defined by at least four points.
30. The non-transitory computer readable media of claim 22 , wherein each of the two or more quadratic curves is defined by at least three points.